Available online 21 July 2015We developed the energy and its analytic gradient for the self-consistent-charge density-functional tight-binding method with the third-order expansion (DFTB3) combined with the fragment molecular orbital (FMO) method, FMO-DFTB3. FMO-DFTB3 reproduced full DFTB3 relative stabilities and the optimized structures of three polyalanine isomers. FMO-DFTB3 was applied to optimize a nano flake of cellulose Iβ, consisting of 10 944 atoms, and a good agreement with the experimental structure was obtained. For a cellulose sheet containing 1368 atoms, FMO-DFTB3 was 43.5 times faster than full DFTB3. The binding between sheets and chains in cellulose was elucidated, and two dispersion models were compared.